Problem: The following line passes through point $(9, -7)$ : $y = -\dfrac{1}{3} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(9, -7)$ into the equation gives: $-7 = -\dfrac{1}{3} \cdot 9 + b$ $-7 = -3 + b$ $b = -7 + 3$ $b = -4$ Plugging in $-4$ for $b$, we get $y = -\dfrac{1}{3} x - 4$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(9, -7)$